“Seven bridges spanned the River Pregel…”

Graph Theory Hymn
Music by Zdenĕk Ryjáček · Lyrics by Bohdan Zelinka · English text by Donald A. Preece
mathematics, graph theory, Leonhard Euler, Eulerian graph, Koenigsberg bridge problem

This video was recorded by MIRKO HORNAK
(Pavol Jozef Šafárik University, Kassa/Košice)
at 6th Workshop on Cycles and Colourings (Stara Lesna, September 11, 1997)

1.Seven bridges spanned the River Pregel,
Many more than might have been expected;
Königsberg’s wise leaders were delighted
To have built such very splendid structures.

2.Crowds each ev’ning surged towards the river,
People walked bemused across the bridges,
Pondering a simple-sounding challenge
Which defeated them and left them puzzled.

3.Here’s the problem; see if you can solve it!
Try it out at home an scraps of paper!
STARTING OUT AND ENDING AT THE SAME SPOT,
YOU MUST CROSS EACH BRIDGE JUST ONCE EACH EV’NING.

Refrain:
Eulerian graphs all have this restriction:
THE DEGREE OF ANY POINT IS EVEN.
That’s the oldest graph result
That mankind has ever known.

4.All the folk in Königsberg were frantic!
All their efforts ended up in failure!
Happily, a learn-ed math’matician
Had his house right there within the city.

5.Euler’s mind was equal to the problem:
“Ah”, he said, “You’re bound to be disheartened.
Crossing each bridge only once per outing
Can’t be done, I truly do assure you.”

Refrain:
Eulerian graphs…

6.Laws of Nature never can be altered,
We can’d change them, even if we wish to.
Nor can flooded rivers or great bridges
Interfere with scientific progress.

7.War brought strife and ruin to the Pregel;
Bombs destroyed those seven splendid bridges.
Euler’s name and fame will, notwithstanding,
Be recalled with Königsberg’s for ever.

Refrain:
Eulerian graphs…

8.Thanks to Euler, Graph Thry is thriving.
Year by year it flourishes and blossoms,
Fertilising much of mathematics
And so rich in all its applications.

9.Colleagues, let us fill up all our glasses!
Colleagues, let us raise them now to toast the
Greatness and the everlasting glory
Of our Graph Thry, which we love dearly!


The acoustic graph

Note

“… well-known problem, which was a curiosity at the time but whose topological nature was later appreciated, in the Koenigsberg bridge problem. In the Pregel, a river flowing through Koenigsberg, there are two islands and seven bridges.

The willagers amused themselves by trying to cross all seven bridges in one continuous walk wihout recrossing any one. Euler, then at St. Petersburg, heard of the problemand found a solution in 1735.

He simplified the representation of the problem by replacing the lands by points A, B, C, D and the bridges joining them by line segments or arcs…”

The question Euler then framed was whether it was possible to describe this figure in the cotinuous motion of the pencil without recrossing any arcs. He proved it was not possible in the above case and gave a criterion as to when such path are or are not possible for given sets of points and arcs.”

(Mathematical Thought, pages 1163—4)

Sources

  • Selected Papers of the 14th British Combinatorial Conference, Keele University, Keele, 5th July—9th July 1993. In: Discrete Mathematics Volume 138, Numbers 1—3, 6 March 1995.
  • EULER, L.: Solutio problematis ad Geometriam situs pertinentis. In: Commentarii Academiae Scientiarum Petropolitanae 8 (1736), pp. 128—140. Issued in 1741.